Diffraction of Electromagnetic Waves by a Circular Aperture in an Infinitely Conducting Plane Screen

The problem of the diffraction of electromagnetic waves by a circular aperture in an infinitely conducting planar screen is studied. Attention is focused chiefly on the low frequency end of the spectrum where the product $ka$ of the wave number k and the aperture radius a is small. Transverse electric and transverse magnetic modal excitation appropriate to the cylindrical geometry of the problem is assumed. New integral representations of the solution corresponding to incident fields of this kind are presented. These representations, which involve a pair of unknown functions, are designed so as to automatically satisfy Maxwell’s equations, the boundary conditions, the radiation condition and all but one of the edge conditions. The unknown functions are shown to satisfy a pair of integrodifferential equations which follow directly from the representations by means of an elementary calculation. Convergent power series solutions of these integrodifferential equations are readily obtained for small $ka$, when it is assumed merely that the excitation is sufficiently regular in the aperture. These results are employed to derive the first terms in the power series expansions of the far fields, the edge fields, the aperture fields and of the transmission coefficients. When the incident transverse electric and magnetic modes are specialized to those which occur in plane wave excitation these expressions are found to reduce to the well-known plane wave formulas obtained by other means.